Basic Math Examples

${(\frac{4 a^{- 6} b^{9}}{14 a^{4} b^{- 3}})}^{0}$

Step 1

Move $a^{- 6}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{4 b^{9}}{14 a^{4} b^{- 3} a^{6}})}^{0}$

Step 2

Multiply $a^{4}$ by $a^{6}$ by adding the exponents.

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Step 2.1

Move $a^{6}$ .

${(\frac{4 b^{9}}{14 (a^{6} a^{4}) b^{- 3}})}^{0}$

Step 2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(\frac{4 b^{9}}{14 a^{6 + 4} b^{- 3}})}^{0}$

Step 2.3

Add $6$ and $4$ .

${(\frac{4 b^{9}}{14 a^{10} b^{- 3}})}^{0}$

Step 3

Move $b^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{4 b^{9} b^{3}}{14 a^{10}})}^{0}$

Step 4

Multiply $b^{9}$ by $b^{3}$ by adding the exponents.

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Step 4.1

Move $b^{3}$ .

${(\frac{4 (b^{3} b^{9})}{14 a^{10}})}^{0}$

Step 4.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(\frac{4 b^{3 + 9}}{14 a^{10}})}^{0}$

Step 4.3

Add $3$ and $9$ .

${(\frac{4 b^{12}}{14 a^{10}})}^{0}$

Step 5

Cancel the common factor of $4$ and $14$ .

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Step 5.1

Factor $2$ out of $4 b^{12}$ .

${(\frac{2 (2 b^{12})}{14 a^{10}})}^{0}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $2$ out of $14 a^{10}$ .

${(\frac{2 (2 b^{12})}{2 (7 a^{10})})}^{0}$

Step 5.2.2

Cancel the common factor.

${(\frac{2 (2 b^{12})}{2 (7 a^{10})})}^{0}$

Step 5.2.3

Rewrite the expression.

${(\frac{2 b^{12}}{7 a^{10}})}^{0}$

Step 6

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 6.1

Apply the product rule to $\frac{2 b^{12}}{7 a^{10}}$ .

$\frac{{(2 b^{12})}^{0}}{{(7 a^{10})}^{0}}$

Step 6.2

Apply the product rule to $2 b^{12}$ .

$\frac{2^{0} {(b^{12})}^{0}}{{(7 a^{10})}^{0}}$

Step 6.3

Apply the product rule to $7 a^{10}$ .

$\frac{2^{0} {(b^{12})}^{0}}{7^{0} {(a^{10})}^{0}}$

Step 7

Simplify the numerator.

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Step 7.1

Anything raised to $0$ is $1$ .

$\frac{1 {(b^{12})}^{0}}{7^{0} {(a^{10})}^{0}}$

Step 7.2

Multiply the exponents in ${(b^{12})}^{0}$ .

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Step 7.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{1 b^{12 \cdot 0}}{7^{0} {(a^{10})}^{0}}$

Step 7.2.2

Multiply $12$ by $0$ .

$\frac{1 b^{0}}{7^{0} {(a^{10})}^{0}}$

Step 7.3

Anything raised to $0$ is $1$ .

$\frac{1 \cdot 1}{7^{0} {(a^{10})}^{0}}$

Step 7.4

Multiply $1$ by $1$ .

$\frac{1}{7^{0} {(a^{10})}^{0}}$

Step 8

Simplify the denominator.

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Step 8.1

Anything raised to $0$ is $1$ .

$\frac{1}{1 {(a^{10})}^{0}}$

Step 8.2

Multiply the exponents in ${(a^{10})}^{0}$ .

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Step 8.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{1}{1 a^{10 \cdot 0}}$

Step 8.2.2

Multiply $10$ by $0$ .

$\frac{1}{1 a^{0}}$

Step 8.3

Anything raised to $0$ is $1$ .

$\frac{1}{1 \cdot 1}$

Step 8.4

Multiply $1$ by $1$ .

$\frac{1}{1}$

Step 9

Divide $1$ by $1$ .

$1$